Final answer:
Standard deviation and mean deviation both measure data spread but do so differently; standard deviation squares deviations before averaging, while mean deviation takes the average of absolute differences. Standard deviation is more widely used for its unique properties and can indicate how data points deviate from the mean.
Step-by-step explanation:
The difference between standard deviation and mean deviation revolves around how they measure the spread of data in a data set. Standard deviation is a measure of how spread out the numbers in a data set are. In calculating the standard deviation, each data point's deviation (difference between the data point and the mean) is squared, summed, and then the square root of that sum is taken. On the other hand, mean deviation, also known as average absolute deviation, is calculated by taking the absolute differences between each data point and the mean, summing these absolute differences, and then dividing by the sample size (n).
The standard deviation is a widely used measure because it has useful properties; for instance, it is always positive or zero and it can be used to determine if a particular data value is close to or far from the mean. When the data points are close to the mean, the standard deviation is small, showing little variation. If the data points are spread out, the standard deviation is larger, indicating more variability. Conversely, mean deviation simply provides an average of these absolute differences without squaring them, which may give a different perspective on the data spread but is less frequently used in statistical analysis.
Both measures include the mean in their calculations; however, the mean is simply the average of all data points. The expected value or mean predicts the long-term average if an experiment is repeated multiple times, while the standard deviation measures the variability of outcomes.